How the Doppler Effect Works

Quick Answer

The Doppler effect is the shift in observed frequency when a source moves relative to an observer. A moving source bunches its wavefronts up ahead and stretches them behind, so an observer it approaches hears a higher frequency and one it has passed hears a lower one. For example, an ambulance siren sounds high then drops as it goes by. The observed frequency approaching is f prime = f v / (v minus vs). Open this simulator, move the source, and watch the wavefronts and the observed frequency respond.

How the Doppler Effect Works

The canvas draws a source that loops across the screen emitting circular wavefronts. When the source sits still the circles are evenly spaced, but when it moves it chases the wavefronts ahead of it. For example, that is why the frequency shifts: each new wavefront ahead starts closer to the observer than the last, so they arrive more often. Behind the source the opposite happens and they arrive less often, giving a lower frequency.

Source Frequency, Wave Speed, and Source Speed

Three quantities set the Doppler shift, and the source frequency is not one that changes.

• Source frequency (f): the pitch the source emits. It stays fixed no matter how fast the source moves.
• Wave speed (v): how fast the wavefronts travel through the medium, unchanged by the source motion.
• Source speed (vs): how fast the source moves. The bigger it is relative to v, the larger the shift.

Calculating the Doppler Shift

To calculate the Doppler shifted frequency for an approaching source, use f prime = f v / (v minus vs); for a receding source, use f v / (v plus vs). To find the observed frequency of a moving source, put in the source frequency, the wave speed, and the source speed. For example, a 440 Hz source moving at 60 m/s through air at 340 m/s is heard near 535 Hz approaching and 372 Hz receding, and the simulator reads both off as you drag the sliders.

Approaching vs Receding, and the Mach Number

Comparing approaching vs receding, the approaching frequency is always higher and the receding one always lower than the source frequency. How big the gap is depends on the Mach number, the source speed divided by the wave speed. For example, a race car at a large fraction of the sound speed gives a dramatic pitch drop, while a slow source barely shifts at all. As the Mach number nears one the wavefronts ahead pile up, the edge of a sonic boom.

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